Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13133209 | C2 | semidirect |
| 3. #16810978 | C2 | direct (N × H) |
| 4. C2×#13133142 | C2 | semidirect |
| 6. C2×C4×C8×C53 | C2 | semidirect |
| 10. #13133209 | C22 | semidirect |
| 16. #13133142 | C22 | semidirect |
| 20. C4×C8×C53 | C22 | semidirect |
| 70. C2×C53 | #488 | semidirect |
| 79. C2×C4×C8 | D53 | semidirect |
| 80. C53 | C2×#488 | semidirect |
| 94. C4×C8 | C2×D53 | semidirect |
| 144. C2 | #16810978 | direct (N × H) |